The present invention relates to an MRI method and an MRI apparatus to implement the method which generates images using MR signals detected by an array of receiver coils. More specifically, the present invention relates to an MRI method and an MRI apparatus to generate a high-resolution image, free of artifacts, in a time-efficient manner. The present invention describes a method for accelerating data acquisition in MRI with N-dimensional spatial encoding.
Nyquist Condition for MRI
Conversion of analog spin induction signals recorded by the received coils to a set of discrete values is termed sampling. For time domain signal a sampling theorem exists, which requires the sampling frequency to exceed the maximum frequency observed in the spectrum of the recorded signal by a factor of two [2]. This is known as Shannon or Nyquist condition. For traditional MRI using linear magnetic field gradients, the time domain variable is replaced with a parameter k, defined as a time integral of the gradient fields applied from the moment of excitation of the spin system. Linearity of the precession frequency dependence in space induced by the linear field gradients defines simple correspondence rules between the time-domain sampling and MRI. For a set of MR signals recorded at a fixed interval Δk, the inverse of the sampling interval in k-space defines the image field of view (FOV) and the inverse of the k-space sampling extent, kmax, defines the image resolution. In order to encode two- or three-dimensional spin density distributions, magnetic field gradients are applied in different dimensions to fill a k-space matrix either in a single k-space trajectory or following multiple excitations.
If the sampling theorem is violated, the spectral components of the original signals will appear at the wrong position in the discrete spectrum representation. This phenomenon is termed aliasing. In the case of MRI, aliasing will appear if the FOV corresponding to the selected k-space sampling interval fails to cover the entire imaged object. Aliasing in the frequency-encoding dimension is typically suppressed by the application of time-domain filtering prior to digitalization of the signals. However, this is not possible for phase encoding dimensions. In the later case, aliasing or folding artifacts occur, which manifest themselves as parts of the object extending past the boundary of the FOV to appear on the other side of the image. In case of Cartesian multidimensional sampling, the aliasing artifacts originating from undersampling in different dimensions are created by a simple multiplication and can be separately treated in the reconstruction, e.g. when specialized alias suppressing reconstruction techniques are applied. These are typically based on utilizing some additional knowledge, either about the object itself or about the structure of the signals, e.g. when coil arrays are used for reception.
Parallel Imaging
The parallel imaging concept was introduced in MRI in 1997 [3] based on employing receiver coil arrays consisting of multiple coil elements and being capable of simultaneous reception of the spin induction signals, where the spatial variation between the sensitivities of the individual elements of the array was used as additional information to encode spatial distributions of the MR signals. Parallel imaging affords a reduction of the data acquisition time with the spatial resolution kept at the original setting. The reduced acquisition time implies undersampling of the k-space data matrix, provided the original full k-space matrix consisted of all the points required to unambiguously encode the selected imaging volume with the given spatial resolution. Undersamling of the data matrix means that not all k-space points are acquired, leading to a spatial aliasing in the images reconstructed using a trivial Fourier transform approach. Reconstruction of the missing information can be accomplished either as unfolding in image space (so-called “Sensitivity Encoding”, SENSE [4]) or directly in k-space by interpolating the missing k-space samples based on the acquired neighboring points using a certain interpolation kernel (so-called GRAPPA approach [5]). The maximum k-space undersampling factor Ri per selected spatial dimension is thus given by a number of coil elements having a variable sensitivity along this dimension. All the previously proposed parallel imaging and reconstruction methods, which do not rely on an a priori information about the imaged sample, have a common feature of employing receiver coil array sensitivities to suppress undersampling artifacts, either explicitly or implicitly [1]. Images originating from typical accelerated MRI acquisitions experience a homogeneous reduction of SNR by a factor of √R, where R is the total acceleration factor, R=R1*R2* . . . . The unfolding process results in the additional spatially-inhomogeneous reduction of SNR, characterized through so-called geometry factor (g-factor). The g-factor depends on the sampling and reconstruction parameters as well as the geometry of the receiver coil array used.
One of the problems arising during implementation of parallel imaging methods originates from the fact that, for the parallel imaging reconstruction to work, coil calibration information needs to be acquired in a manner consistent with the actual imaging scan. For the implementations relying on a separate calibration scan, this consistency can easily be broken via dynamic processes in the imaged object, motion or scanner instability. That is why, in addition to the currently standard pre-scan-based coil calibration, where coil sensitivity information is acquired before or after the actual imaging scan, a so-called auto-calibrating approach is often employed, where a certain area of the k-space matrix (typically close to the k-space origin) is sampled densely to satisfy the Nyquist conditions for the given FOV. These additional k-space samples are often referred to as auto-calibrating scans (ACS). The requirement to calibrate coil sensitivities slows down the total acquisition time or results in an additional decrease in SNR of the reconstructed images if the total acquisition time is kept constant via an additional increase in the acceleration factor. Additionally, both separate pre-scan and integrated auto calibration methods are incompatible with certain MRI acquisition methods, like echo planar imaging (EPI), acquisitions with a continuously moving table and many more.
SENSE (Sensitivity Encoding)
Parallel imaging principles are best visualized with the example of the image-space methods, such as SENSE [4]. Image reconstruction in SENSE starts with a direct 2D or 3D fast Fourier transform (FFT) of the undersampled data resulting in an MR image with a reduced FOV. In case that this reduced FOV is smaller than the entire imaged object, which is typically the case for accelerated acquisitions, FOV aliasing artifacts occur which manifest themselves as folding of the object along the corresponding dimension. At this step SENSE reconstruction is applied, which attempts to unfold the aliased image on a pixel-by-pixel basis. This is only then possible, because the image data from each individual receiver coil are modulated with the spatially varying sensitivity of the coil and this modulation occurs prior to the folding of the image. Provided the coil modulation functions are known during reconstruction, it is possible to calculate the weighted aliasing patterns and solve for the original pixel intensities. Hence, classical SENSE reconstruction requires the accurate knowledge of the receiver coil sensitivities and produces one composite image. Fortunately, coil sensitivity profiles are relatively smooth, which makes it possible to perform the sensitivity estimation based on a relatively quick low-resolution calibration scan, including consecutive acquisitions of the same object with the array coil and a volume (body) coil, respectively. If no volume coil is available for the measurement, it is possible to determine relative coil sensitivities, with regard to either one of the array coils or a combination thereof, which is often referred to as relative SENSE (rSENSE) [6] or modified SENSE (mSENSE) [7]. It is possible to implement both rSENSE and mSENSE as auto-calibrating techniques, where the central k-space region of the actual accelerated acquisition is sampled densely to produce a low-resolution full FOV image for coil sensitivity calibration.
GRAPPA (GeneRalized Autocalibrating Partially Parallel Acquisition)
In contrast to the above, the k-space-based GRAPPA approach [5] decouples the image unfolding steps from the coil combination, which allows one to optimize separately the unfolding process as well as the subsequent combination of the individual coil images. For this reason, GRAPPA has become one of the most robust and frequently used parallel imaging methods.
Unaliasing in GRAPPA takes place in k-space via interpolation of the missing k-space samples based on the acquired neighboring scans. The interpolation kernel is described by so-called coil weighting coefficients, which for the given undersampling pattern are defined by the coil sensitivity profiles. The number of coefficients or, in other words, the extent of the interpolation kernel in k-space affects both the reconstruction speed and the artifact suppression quality. The extent of the kernel is selected such that it covers at least several sampled “source” k-space points to calculate the given missing “target” k-space point.
Coil weighting coefficients are typically defined based on the small portion of fully sampled k-space data, 16 to 32 lines for a typical 1D-acceleration case, which can either be acquired separately or integrated into the actual imaging scan in the form of ACS lines. The necessity of coil weighing calibration significantly hampers the scan time advantage gained via the parallel imaging acceleration, e.g. for an imaging scan with a nominal acceleration factor of 4 and 32 ACS lines, the true acceleration factor accounts only to 2.67. GRAPPA implementations with integrated ACS lines typically incorporate the ACS data into the k-space matrix, which allows for a certain improvement in the SNR of the resulting images. However, the high resolution portion of the data is still affected by the g-factor-related SNR penalty corresponding to the nominal acceleration factor.
“Phase-Scrambled” MRI
In the early days of MRI it was observed, that application of a quadratic phase modulation in object space leads to a dramatic transformation of the k-space signal appearance [8,9]. It was proposed to employ quadratic phase modulation to relax dynamic range requirements of the analog-to-digital converters (ADC) or digital-to-analog converters (DAC) as well as to reduce the peak power of the RF power amplifier. The term “phase scrambling” refers to the property of the signals, which, due to the presence of the phase modulation, remain mixed with almost random phase weighting factors and never add up constructively, independent of the k-space position.
Later, properties of k-space signals recorded in the presence of quadratic phase modulation across the imaged object were examined in detail [10]. Based on the observation made, new image reconstruction algorithms were proposed, which amongst other findings, were shown to have pronounced alias-suppressing properties. Recently, an alternative reconstruction algorithm of phase-scrambled MRI data was proposed, based on the Fresnel transformation [11], which allows for a relatively free scaling of the image FOV and suppressed the arising aliasing artifacts to a large extent. It has been shown, that upon employing an appropriate quadratic phase modulation, it is for example possible to reconstruct an 128-pixel image with the original nominal FOV from a k-space dataset with a nominal size of 256 pixels undersampled by a factor of 2. In other words from k-space 128 samples it is possible to reconstruct 128 image pixels, where quadratic phase modulation in the object domain allows for a flexible selection of image resolution and FOV during the reconstruction. Under idealized conditions, both resolution and SNR of thus reconstructed images approach the respective parameters of the traditional Fourier-encoded acquisitions with the equal matrix size.
In view of these aspects of prior art, it is the object of the present invention to introduce a method for accelerating data acquisition in MRI with N-dimensional spatial encoding to generate a high-resolution image free of artifacts in a time-efficient manner.